Polynomial Equations
A polynomial equation is any equation that contains a polynomial expression.
The degree of a polynomial equation is the degree of the polynomial expression in the
equations.
2x2 + 5x + 3 = 0 is a second degree polynomial equation.
The zero-product property states that if the product of two numbers is zero, then one of
those numbers must be zero. If your answer to a multiplication problem is zero, then one of
the numbers you are multiplying (factors) must be zero.
A quadratic equation is an equation in the form ax2 + bx + c = 0 where a, b and c are real
numbers and a  0. When it is written in descending order of exponent like this, it is said to
be in standard form. Since the left-hand side is a 2nd degree polynomial, these are also
sometimes known as second-degree equations.
Steps for solving a quadratic equation by factoring
1.
2.
3.
4.
5.
Make sure the polynomial is in standard form and equals zero.
Factor the polynomial
Set each of the factors equal to zero
Solve those two little equations
Check your answers by substituting back into the original.
Remember: As soon as you see a square and an equal sign:


Drag everything to the left and put the terms in order
Expect 2 answers
Solving higher order equations by factoring
w3 + 5w2 – 4w – 20 = 0
3rd degree – expect 3 answers
w2(w + 5) – 4(w + 5) = 0
(w + 5)(w2 – 4) = 0
(w + 5)(w + 1)(w – 1) = 0
w+5=0|w+1=0|w–1=0
w = -5 |
w = -1 |
w=1
Solving equations involving polynomial functions
f(x) = x2 – 5x + 4 for what values of x does f(x) = 4?
x2 – 5x + 4 = 4
x2 – 5x + 4 – 4 = 0
x2 – 5x = 0
x( x – 5) = 0
x=0|x–5=0
x=0|
x=5
Finding the zeros of a function
You are finding the values of x when y = 0. In other words, where the graph crosses the xaxis.